Millisecond pulsars (MSPs) orbiting helium white dwarfs (WDs) in eccentric orbits challenge the established binary evolution paradigm that predicts efficient orbital circularization during the mass transfer episode that spins up the pulsar. Freire and Tauris (2014) recently proposed that these binary MSPs may instead form from the rotationally delayed accretion-induced collapse of a massive WD. This scenario predicts that eccentric systems preferably host low-mass pulsars and travel with small

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... ystemic velocities - in tension with new observational constraints. Here, I show that a substantial growth in eccentricity may alternatively arise from the dynamical interaction of the binary with a circumbinary disk. Such a disk may form from ejected donor material during hydrogen flash episodes, when the neutron star is already an active radio pulsar and tidal forces can no longer circularize the binary. I demonstrate that a short-lived (10^4-10^5 yr) disk can result to eccentricities of e∼0.01-0.15 for orbital periods between 15 and 50 days. Finally, I propose that, more generally, the disk hypothesis may explain the lack of circular binary pulsars for the aforementioned orbital-period range.